Question

Find the common ratio r for the following geometric sequence.

{1, 5, 25, 125, 625,...}
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Answer 1

In this sequence, the common ratio (r) is 5, as each term is obtained by multiplying the previous term by 5.

Explanation:

In a geometric sequence, the common ratio (r) is found by dividing any term by the previous term. Let's calculate it for the given sequence:

r = 5 / 1 = 25 / 5 = 125 / 25 = 625 / 125

Now, simplify these ratios:

r = 5

r = 5

r = 5

r = 5

In this sequence, the common ratio (r) is 5, as each term is obtained by multiplying the previous term by 5.